Yet this is the marvelous case of the new Roundabout Theatre production of Richard Adler and Jerry Ross’ 1954 “The Pajama Game,” which opened last night at the company’s American Airlines Theatre.

It stars an absolutely revelatory Harry Connick Jr. and is staged and choreographed with amazing grace and zest by Kathleen Marshall. And did I mention Harry Connick Jr.?

The success is remarkable not least because of the oddball story: an averted union strike in a pajama factory in Cedar Rapids, Iowa. And the score, while containing a few standards, is hardly legendary Broadway fare.

But the show – the old book has been niftily adapted by Peter Ackerman – is also unusually funny, and with giddy assurance Marshall whirls around both comedy and cast.

Martin Pakledinaz’s costumes are period-perfect without looking quaint; Peter Kaczorowski’s lighting doesn’t put a beam out of place, while Derek McLane’s almost cartoonish scenery provides a charming setting for all the high jinks.

And high jinks just about describes a romp that somehow evokes a Broadway where critics expected to be tickled to death and audiences fell into aisles with helpless laughter.

Indeed, Marshall deserves the rank of Field Marshal for the way she deploys her troops – and not least in the choreography.

Original co-director Jerome Robbins was responsible for supervising dances, and actually created some, but most credit went to Bob Fosse making a memorable Broadway debut.

But Marshall has neither followed nor copied them – except almost inevitably for a Fosse homage in “Steam Heat.” The dances, particularly in the wildly inventive “Hernando’s Hideaway,” are simply dazzling.

The performers are the purest delight, and it’s difficult to know where to start handing over the bouquets. Richard Poe is sneakily duplicitous as the factory owner, Peter Benson makes a bouncey little union leader intent on not getting cheated, and Joyce Chittick is a knockout as his girl Mae, a plain Jane who doffs her specs – and skirt – to raise “Steam Heat.”

Though it was originally danced by the boss’ secretary Mabel, the new Mabel is now the handsomely statuesque Roz Ryan, who acts up a storm and sings but doesn’t dance.

As the pathologically jealous Hines, Michael McKean is a gem whether drunkenly throwing knives or offering the neatest of soft-shoes.

Kelli O’Hara is nicely tough with a beautifully soft center as the heroine Babe and sings most exquisitely, making Connick a perfect foil.

But the absolute standout – Connick apart – was Megan Lawrence as Hines’ sidekick, Gladys, who would be worth a Tony Award simply for the manic enthusiasm she throws to the winds and a hapless Connick in “Hernando’s Hideaway.”

So how about Connick? After composing the most underrated Broadway score in the last 20 years (“Thou Shalt Not”), in his musical theater stage debut he is absolutely sensational. One disturbing point – close your eyes and you might think he was channeling Frank Sinatra.

But then, what the hell – he sounds so true and natural that it could almost be Sinatra channeling Connick. He’s bright, funny, plays a mean piano and can even dance. This is a debut of legendary proportions.

And in the roustabout finale, O’Hara and Connick admirably show that, with the right pair, pajamas can fit quite perfectly.

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THE PAJAMA GAME

[*** 1/2] (Three and one-half stars)

The Roundabout Theatre Company at the American Airlines Theatre, 227 W. 42nd St.; (212) 719-1300.